Synthetic aperture radar (SAR) is a technique whereby multiple pulses from a moving radar are coherently combined to form an image while achieving an azimuth resolution much finer than the beamwidth of the radar's real antenna. Range resolution is a function of radar signal bandwidth. Image formation is typically a computationally intensive operation. SAR design consequently favors transform techniques that ultimately only approximate the matched filter for each pixel location in the image. The approximations tend to be most accurate at the image focal point, nominally its center. Large scenes with relatively coarse resolutions tend to exhibit artifacts resulting from approximations to the spherical wavefronts. Small scenes at finer resolutions suffer more from range migration effects.
The Polar Format Algorithm (PFA) is a well-known technique for spotlight SAR image formation. It recognizes that the raw Linear FM (LFM) SAR data, when de-chirped, represent sample points in the Fourier space of the scene being imaged, most accurately at the scene center, but suitably so for a significant neighborhood around the scene center, often for up to several thousand pixels depending on range and wavelength. At near ranges and longer wavelengths the focused image sizes may be substantially reduced. However, those raw data sample points are nominally on a polar grid in Fourier space, and need to be resampled to a rectangular grid for efficient processing with digital computers. This resampling is termed polar reformatting, hence the name Polar Format processing. FIG. 1 illustrates processing steps that implement conventional PFA. The familiar range and azimuth alignment operations are respectively performed at 11 and 13, followed by a two-dimensional DFT. The range alignment operation is shown by broken line to indicate that this part of the PFA process can, as is known in the art, be alternatively accomplished with conventional real-time motion compensation.
Although the resampling operation of PFA mitigates the problematic range migration, residual effects of wavefront curvature still manifest themselves as spatially variant distortions and image quality degradation, generally worsening in the image with pixel distance from the scene center. In fact, a threshold on tolerance for image degradation imposes a scene size limit for a focused SAR image. This limit is known in the art.
Some recently developed SAR systems have been operated in a manner to form images larger than the classical limits suggested for the Polar Format Algorithm (PFA). Such systems routinely operate with image dimensions (e.g., several thousand pixels by several thousand pixels) that often exceed the focused scene size limits for PFA processing. The desire for future operational systems to operate with ever-larger images at ever-finer resolutions exacerbates this problem.
Subaperture techniques combined with PFA have been shown effectively to mitigate wavefront curvature effects and substantially increase focused scene diameter. These techniques are implemented within image formation algorithms and are generally not suitable for application to an already processed image, unless the original image formation processing is first undone.
One conventional technique for post-processing PFA images applies a spatially variant filter to an already formed image, thereby correcting the misfocus due to residual wavefront curvature effects. This technique is sometimes referred to as Polar Formatting with Post Filtering (PF2) processing. However, the technique is designed for a linear flight path, and therefore has correspondingly limited robustness over imaging geometry.
It is desirable in view of the foregoing to provide for mitigation of a wavefront curvature effect in an already-formed radar image, without the aforementioned flight path limitations.